Problem: What number could replace $r$ below? $\dfrac{1}{10} = \dfrac{r}{100}$
Solution: The fraction on the left represents 1 out of 10 slices of a rectangular cake. What if we cut the cake into 100 slices instead? How many slices would result in the same amount of cake? We would need 10 slices. $\dfrac{1}{10} = \dfrac{10}{100}$ and so the answer is $10$ Another way to get the answer is to multiply by $\dfrac{10}{10}$ $\dfrac{10}{10} = \dfrac{1}{1} = 1$ so really we are multiplying by 1. The final equation is: $\dfrac{1}{10} \times \dfrac{10}{10} = \dfrac{10}{100} $ so our answer is $10$.